The assembly of a fiber end with a lens for producing a substantially parallel beam from light emerging from the fiber end is called a “collimator.” The lens could be a gradient index (GRIN), refractive, or diffractive lens. Herein, the focus is on a collimator incorporating a GRIN lens. The GRIN lens has an index of refraction that gradually varies from the axis of the lens towards the outer periphery of the lens. In a GRIN lens, rays of light follow sinusoidal paths whose trajectory is defined in terms of pitch. One pitch is equivalent to the light traversing one sinusoidal cycle and can be expressed as follows:                     P        =                              L            ⁢                          A                                            2            ⁢                                                  ⁢            π                                              (        1        )            where P is pitch, √{square root over (A)} is index gradient parameter, and L is length of the lens.
The collimator is assembled by placing the fiber end a distance from the lens. The fiber-to-lens distance is determined by the back focal length (BFL) of the GRIN lens, which can be expressed as follows:                     BFL        =                              1                                          N                o                            ⁢                              A                                              ⁢                                          ⁢                      cot            ⁡                          (                              L                ⁢                                  A                                            )                                                          (        2        )            where no is on-axis index of refraction of the lens, √{square root over (A)} is index gradient parameter, and L is length of the lens. Both No and √{square root over (A)} are functions of wavelength. The dependence of No on wavelength can be expressed as follows:                               N          o                =                  B          +                      C                          λ              2                                                          (        3        )            where B and C are constants depending on the lens material. The dependence of √{square root over (A)} on wavelength can be expressed as follows:                               A          ⁡                      (            λ            )                          =                              [                                          K                0                            +                                                K                  1                                                  λ                  2                                            +                                                K                  2                                                  λ                  4                                                      ]                    2                                    (        4        )            where K0, K1, and K2 are constants depending on the lens material.
Ideally, the fiber-to-lens distance is such that the collimator operates with low insertion loss. It is common practice to tune the collimator to operate efficiently at a particular design wavelength. However, the BFL of the GRIN lens varies from one wavelength to another due to chromatic dispersion. Thus, if a collimator tuned to operate efficiently at a particular design wavelength is used at a wavelength other than the design wavelength, there would be an offset in BFL. If the fiber-to-lens distance is not adjusted to compensate for this offset, the collimator could have excessive insertion loss, particularly if there is a great disparity between the design wavelength and the operating wavelength. As can be appreciated, the need to readjust the fiber-to-lens distance for each operating wavelength complicates use of the collimator in multi-bandwidth applications.
From the foregoing, a collimator that can operate efficiently at multiple wavelengths without having to readjust the fiber-to-lens distance at each wavelength is desired.